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A smooth Monte Carlo approach to joint chance-constrained programs

Author

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  • Zhaolin Hu
  • L. Hong
  • Liwei Zhang

Abstract

This article studies Joint Chance-Constrained Programs (JCCPs). JCCPs are often non-convex and non-smooth and thus are generally challenging to solve. This article proposes a logarithm-sum-exponential smoothing technique to approximate a joint chance constraint by the difference of two smooth convex functions, and uses a sequential convex approximation algorithm, coupled with a Monte Carlo method, to solve the approximation. This approach is called a smooth Monte Carlo approach in this article. It is shown that the proposed approach is capable of handling both smooth and non-smooth JCCPs where the random variables can be either continuous, discrete, or mixed. The numerical experiments further confirm these findings.

Suggested Citation

  • Zhaolin Hu & L. Hong & Liwei Zhang, 2013. "A smooth Monte Carlo approach to joint chance-constrained programs," IISE Transactions, Taylor & Francis Journals, vol. 45(7), pages 716-735.
    • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:7:p:716-735
    DOI: 10.1080/0740817X.2012.745205
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    Cited by:

    1. Zhou, Liping & Geng, Na & Jiang, Zhibin & Wang, Xiuxian, 2017. "Combining revenue and equity in capacity allocation of imaging facilities," European Journal of Operational Research, Elsevier, vol. 256(2), pages 619-628.
    2. Xiaodi Bai & Jie Sun & Xiaojin Zheng, 2021. "An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1056-1069, July.
    3. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    4. L. Jeff Hong & Zhaolin Hu & Liwei Zhang, 2014. "Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 385-400, May.
    5. Shanshan Wang & Jinlin Li & Sanjay Mehrotra, 2021. "Chance-Constrained Multiple Bin Packing Problem with an Application to Operating Room Planning," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1661-1677, October.

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